Harmony is not a "second sound you hear". It is the context created by the combination of all the sounds you hear. Even music with a single melodic line---e.g. unaccompanied violin or solo singer---has harmony despite its not even having a second sound. Do not confuse "harmony" with "accompaniment".
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Alex BassonJan 7 '13 at 14:30

9 Answers
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The basis of counterpoint (point against point) is melody. Harmony is evident in counterpoint which, I suppose, is what is causing the confusion. A theory professor once told me that Harmony is a byproduct of the rules of counterpoint being used properly. Counterpoint changed from renaissance to baroque in some significant ways. Renaissance counterpoint is often referred to as melodic counterpoint while Baroque is referred to as Harmonic counterpoint.

Composers who used counterpoint (renaissance period composers) did not think about the harmony in terms of chords, our modern sense of harmony. The melodic lines that were created using these counterpoint rules resulted in something that we can perceive as chords. However their focus was solely on melodies and the way they interacted. Baroque counterpoint is structurally based around chords but the focus is still on melodic interaction.

One trick that is very commonly used in counterpoint is imitative counterpoint. In this trick a melody is introduced in one voice. After the melody is completed, the same melody (often beginning at the interval of a fifth above the original melody) is introduced in a different voice while the first voice moves on to a secondary or counter-melody.

Listen for these types of thematic devices. The melodies will be very pronounced. Instead of hearing chords being sustained under a melodic line you will hear multiple melodies in multiple voices that come together to create a unique kind of harmony.

I liked your answer a lot. Can you please point some good reading material about composing counterpoint in the renaissance form (ie, based on melody rather than harmony)?
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Alejandro IglesiasMay 30 '12 at 2:52

I think the difference you would hear would be the difference in the direction and rhythm of the lines. Counterpoint would fill in the melodic "gaps" rhythmically and harmonically. Basic harmony often lines up with the melody. Counterpoint frequently goes opposite the melody, thus its name.
Listen to some Baroque music, where counterpoint was used heavily (Bach is great for this). Later periods of music still used it, but didn't rely on it so much as in the Baroque.

Counterpoint is one of the reasons I have always enjoyed playing Bach. The 2nd part is not secondary and just harmony with the 1st part. It stands on its own and often crosses the 1st part, making is fun to play.
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jwernernyAug 19 '11 at 17:36

Harmony refers only to the relative pitches of the different voices you hear sounding together in a nice way; it says nothing about the timing of the notes in the different voices.

Counterpoint refers to different voices forming their own separate melodies: (many of) their notes are produced at different times and with different durations. Counterpoint will (in all cases that I've heard) create harmony, but a lot of music with harmony only has a single voice with a melody, in which case there is no counterpoint. Polyphony is the extreme form of counterpoint where all voices sing separate melodies. In extreme cases, the melodies are actually completely different songs (e.g. In feuers hitz and O rosa bella, from the Glogauer songbook), but even then, they are usually combined in such a way that the result is in harmony.

Of course, there are all kinds of mixtures: for instance, a canon, in which all voices have the same melody, only shifted in time.

In the old days, when mr. Bach was doing his thing, harmony as we know it didn't really exsists in the same way. Ofcourse, multiple-sounding-notes are creating a harmony. But it wasn't a harmony like we hear now in pop and jazz (etc...)

So: if you have a jazz tune in C and the melody goes: E-F-G and the bass player plays C-D-E then there is a big change the piano/guitar player plays: Cmaj7, Dmin7, Emin7.
This is vertical.

If Bach wrote: E-F-G and wrote in the bass C-D-E he didn't mean Cmaj7, Dmin7, Emin7 he just meant them to go together.
This is horizontal

Then there is something else, counterpoint is a set of rules most of them influenced by church. Google for consonant, dissonant etc. Nowadays you can do whatever you want (thanks to enlightenment! Jeej!) but back in the days, you couldn't.

So, why studie counterpoint and harmony?
Well, harmony is obvious; music of today works on 'harmony'
Counterpoint is nice to studie so you can learn to work in a framework. Maybe you're even able to create your own! Like the 12 tone system Schoenberg created (http://en.wikipedia.org/wiki/Twelve-tone_technique)
* - if you do this, please mention it at music.stackexchange ;-)

I have to take issue with the implication that Bach wasn't aware of or intentional about his use of harmony, as "he just meant them to go together" implies. He meant them to go together because he deeply understood the harmonic consequences of superimposing those lines. His use of harmony was no accident; rather it was the product of someone who completely understood what he was doing.
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Alex BassonJan 7 '13 at 14:24

I think @AlexBasson is correct. In fact, the Cmaj7, Dmin7, Emin7 is not more vertical than the Bach example either. It's just written that way because that's an easy way to communicate to the player (without writing out the complete voicing). But in both cases the middle chord is just a passing chord and doesn't really have a harmonic function (so you could call it "horizontal"). There isn't really much difference between (classical) jazz and Bach except that the rules are less strict. But it's functional harmony in both cases.
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hermanDec 16 '14 at 0:11

Think of counterpoint as a group of independent melodies that overlap and happen simultaneously, yet are designed to create a consonant effect.

Think of harmony as what happens when you strum a series of chords in a progression on the guitar.

Most music nowadays has one melody and chords underneath it to support it. But in earlier times counterpoint was more prevalent. Counterpoint tends to be a great deal more intricate and difficult to compose effectively, by the way.

Counterpoint is the simultaneous combination of relatively independent musical lines. Hey, I think I just remembered the definition word-for-word from our AP Theory book! Haha. Well, lines of harmony usually go with the melody in the same rhythm, and somewhat the same direction. Contrapuntal lines are almost completely different, but sound good together.

There are two types of harmony: vertical and linear. The linear form would "imply" harmony depending on which tones are used in which sequence. The vertical harmony (chords) would be a more direct form, because more notes are used, therefore more context. But even this form of harmony does have a linear component, because harmony is not just the information that is contained in single chord - it also contains the information that is included in tones/chords that come before and after.

Counterpoint, because it is two or more tones played simultaneously, is a subset of vertical harmony.

My personal opinion is that modern concepts of Western harmony are more than adequate for explaining what's going on with traditional counterpoint as it occurred during the Baroque and Classical eras.

Harmony is always there whether it is single line music or multiline music. The difference is just the way it is presented. Harmony could be effectively used in all types of music. It is a fact that music is created basically with a melody. Of course, the melody has a sweetness. This abstract quality will be fortified when it is harmonized, and again it will be sweetest when packed with counter parts. Harmony is an ocean over which the vessel of counter part glides with the sailor called melody.